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Mirrors > Home > ILE Home > Th. List > fv3 | Unicode version |
Description: Alternate definition of the value of a function. Definition 6.11 of [TakeutiZaring] p. 26. (Contributed by NM, 30-Apr-2004.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
fv3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfv 5387 | . . 3 | |
2 | bi2 129 | . . . . . . . . . 10 | |
3 | 2 | alimi 1416 | . . . . . . . . 9 |
4 | vex 2663 | . . . . . . . . . 10 | |
5 | breq2 3903 | . . . . . . . . . 10 | |
6 | 4, 5 | ceqsalv 2690 | . . . . . . . . 9 |
7 | 3, 6 | sylib 121 | . . . . . . . 8 |
8 | 7 | anim2i 339 | . . . . . . 7 |
9 | 8 | eximi 1564 | . . . . . 6 |
10 | elequ2 1676 | . . . . . . . 8 | |
11 | breq2 3903 | . . . . . . . 8 | |
12 | 10, 11 | anbi12d 464 | . . . . . . 7 |
13 | 12 | cbvexv 1872 | . . . . . 6 |
14 | 9, 13 | sylib 121 | . . . . 5 |
15 | exsimpr 1582 | . . . . . 6 | |
16 | df-eu 1980 | . . . . . 6 | |
17 | 15, 16 | sylibr 133 | . . . . 5 |
18 | 14, 17 | jca 304 | . . . 4 |
19 | nfeu1 1988 | . . . . . . 7 | |
20 | nfv 1493 | . . . . . . . . 9 | |
21 | nfa1 1506 | . . . . . . . . 9 | |
22 | 20, 21 | nfan 1529 | . . . . . . . 8 |
23 | 22 | nfex 1601 | . . . . . . 7 |
24 | 19, 23 | nfim 1536 | . . . . . 6 |
25 | bi1 117 | . . . . . . . . . . . . . 14 | |
26 | ax-14 1477 | . . . . . . . . . . . . . 14 | |
27 | 25, 26 | syl6 33 | . . . . . . . . . . . . 13 |
28 | 27 | com23 78 | . . . . . . . . . . . 12 |
29 | 28 | impd 252 | . . . . . . . . . . 11 |
30 | 29 | sps 1502 | . . . . . . . . . 10 |
31 | 30 | anc2ri 328 | . . . . . . . . 9 |
32 | 31 | com12 30 | . . . . . . . 8 |
33 | 32 | eximdv 1836 | . . . . . . 7 |
34 | 16, 33 | syl5bi 151 | . . . . . 6 |
35 | 24, 34 | exlimi 1558 | . . . . 5 |
36 | 35 | imp 123 | . . . 4 |
37 | 18, 36 | impbii 125 | . . 3 |
38 | 1, 37 | bitri 183 | . 2 |
39 | 38 | abbi2i 2232 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wceq 1316 wex 1453 wcel 1465 weu 1977 cab 2103 class class class wbr 3899 cfv 5093 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 |
This theorem is referenced by: (None) |
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